The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1
 0 X^2  0 X^2  0 X^2 2X^2 2X^2 2X^2  0  0 X^2 X^2
 0  0 X^2 2X^2 2X^2 X^2  0 X^2 2X^2  0 X^2 2X^2 X^2

generates a code of length 13 over Z3[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+12x^24+216x^26+8x^27+4x^30+2x^39

The gray image is a linear code over GF(3) with n=117, k=5 and d=72.
This code was found by Heurico 1.16 in 0.000464 seconds.